Journal article Open Access

# $\text {L}^2$-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov–Poisson–Fokker–Planck System

Addala, Lanoir; Dolbeault, Jean; Li, Xingyu; Tayeb, M. Lazhar

### Citation Style Language JSON Export

{
"DOI": "10.1007/s10955-021-02784-4",
"container_title": "Journal of Statistical Physics",
"title": "$\\text {L}^2$-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov\u2013Poisson\u2013Fokker\u2013Planck System",
"issued": {
"date-parts": [
[
2021,
6,
21
]
]
},
"abstract": "This paper is devoted to the linearized Vlasov\u2013Poisson\u2013Fokker\u2013Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar product adapted to the presence of a Poisson coupling. Our framework provides estimates which are uniform in the diffusion limit. As an application in a simple case, we study the one-dimensional case and prove the exponential convergence of the nonlinear Vlasov\u2013Poisson\u2013Fokker\u2013Planck system without any small mass assumption.",
"author": [
{
},
{
"family": "Dolbeault, Jean"
},
{
"family": "Li, Xingyu"
},
{
"family": "Tayeb, M. Lazhar"
}
],
"volume": "184",
"type": "article-journal",
"issue": "1",
"id": "5747811"
}
20
15
views